Regional Phase Amplitude Tomography for Seismic Verification

Tomography Method

Amplitude model:

aijk = ck f(mbi) sjk xij -bk e -akxij,

i, j, k	represent source, site and phase type
ck      source generation
f       source scaling (taken as known function of mb)
sj      site effect
xij     distance
bk      spreading
ak      spatial attenuation
Take logarithms, correct for source scaling and discretize attenuation:
Dijk = Ck + Sjk - bk log10xij - log10 e Sm akm dxijm,

m       represents discretization

Form phase ratios:
DDij = DC + DSj - Dblog10xij - log10 e Sm Dam dxijm.
Write in matrix form:
Ax = d
Solve using least squares:
x = (AtWtWA + St L2S)-1 AtWtd,

S      represents regularization equations 
L      regularization weights
W      1/data error

Calculate resolution, covariance and prediction error using standard formulae.

Attenuation was discretized using an array of ellipses.


Cover | Introduction | Data | Tomography Method | Results | Summary